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How do you find the derivative of #f(x)=e^(2x)#?

Answer 1

Cameron Alexander

#f'(x)=2e^(2x)#

If #f(x)=e^(g(x))# then #f'(x)=g'(x)e^(g(x))#

#g(x)=2x# #g'(x)=2#

#f'(x)=g'(x)e^(g(x))=2*e^(2x)=2e^(2x)#

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Answer 2

Aurora Alvarado

To find the derivative of ( f(x) = e^{2x} ), use the chain rule, which states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

The derivative of ( e^{2x} ) with respect to ( x ) is ( 2e^{2x} ). So, the derivative of ( f(x) = e^{2x} ) is ( f'(x) = 2e^{2x} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.